In this paper, we present a new method to generate an instantaneous volumetric image using a single x-ray projection. To fully extract motion information hidden in projection images, we partitioned a projection image into small patches. We utilized a sparse learning method to automatically select patches that have a high correlation with principal component analysis (PCA) coefficients of a lung motion model. A model that maps the patch intensity to the PCA coefficients is built along with the patch selection process. Based on this model, a measured projection can be used to predict the PCA coefficients, which are further used to generate a motion vector field and hence a volumetric image. We have also proposed an intensity baseline correction method based on the partitioned projection, where the first and the second moments of pixel intensities at a patch in a simulated image are matched with those in a measured image via a linear transformation. The proposed method has been valid in simulated data and real phantom data. The algorithm is able to identify patches that contain relevant motion information, e.g. diaphragm region. It is found that intensity correction step is important to remove the systematic error in the motion prediction. For the simulation case, the sparse learning model reduced prediction error for the first PCA coefficient to 5%, compared to the 10% error when sparse learning is not used. 95th percentile error for the predicted motion vector is reduced from 2.40 mm to 0.92mm. In the phantom case, the predicted tumor motion trajectory is successfully reconstructed with 0.82 mm mean vector field error compared to 1.66 mm error without using the sparse learning method. The algorithm robustness with respect to sparse level, patch size, and existence of diaphragm, as well as computation time, has also been studied.
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